The invention is concerned with certain new and useful improvements in steps of this character which have been previously proposed. In U.S. Pat. No. 3,627,350, granted to Denver F. Cross, Jul. 14, 1971, a bumper step is disclosed which in one position functions as a horizontally rearwardly extending tread plate and in a second position disposes the tread plate in inverted position above the generally horizontal upper surface of the bumper. This angular bumper step has not, to applicant's knowledge, enjoyed significant commercial favor and the present inventor believes that one reason for this is that, in both positions, the step will move and rattle when traversing rough roadways and rough terrain. In fact, not only will noisy and annoying rattling occur with this prior art construction, which I incorporate herein by reference, the bouncing and jouncing of the truck may well cause the step to swing down from its upper position.